Solve 3rd Taylor Polynomial for (x-1)In(x) About x0=1 - Find Error Bound

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Homework Help Overview

The problem involves finding the third Taylor polynomial for the function f(x) = (x-1)ln(x) about x0 = 1, and using this polynomial to approximate f(0.5). Additionally, the task includes determining the upper bound for the error between the approximation and the actual function value.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the third Taylor polynomial and the evaluation of the approximation at a specific point. There is a question regarding the notation used in the function, specifically the clarification of 'In(x)' as 'ln(x)'.

Discussion Status

The discussion is ongoing, with some participants providing clarifications and others sharing their results. There is no explicit consensus on the correctness of the calculations, and questions about finding the actual error remain open.

Contextual Notes

Participants express confusion regarding the textbook's clarity and mention the absence of guidance from the teacher, which may impact their understanding of the problem.

Newbatmath
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Hey guys! I am attempting to do this problem and have been working with it for awhile now. Once again, it is an issue of the textbook not being very clear and making me more confused than ever. Sadly, our teacher is still MIA.

Find the third Taylor polynomial P3(x) for the function f(x)= (x-1)In(x) , about x0 = 1; and use p3(0.5) to approx. f(0.5). Find the upper bound for error /f(0.5) – p3(0.5)/, then compare it to the actual error.

I know this is a tall order but any help you could give me that I could compare to my work here would be such a help! Thanks a bunch!
 
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What is the 'In(x)' in your function. Do you mean 'ln(x)'?

Otherwise this question is very straightforward. Just calculate the first 3rd Taylor polynomial and plug in numbers.

I don't see the problem?
 
Yep, you are right. ln(x). Sorry about that. :) Thanks so much!
 
Okay so I somehow got -4.25. Does anyone else think that is correct?

Anyone know how to find the actual error?
 

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